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# help

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140
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Order from greatest to least
a) 25^100
b) 2^300
c) 3^400
d) 4^200
e) 2^600

Aug 25, 2018

#1
+3

Since there is no common base number, we will have to make a common exponent number. The GCF of all of these exponents is \(100\), so lets make all of the exponents \(100\). We have:

a) \({25}^{100}\)

b) \({2}^{3(100)} = {8}^{100}\)

c) \({3}^{4(100)} = {81}^{100}\)

d) \({4}^{2(100)} = {16}^{100}\)

e) \({2}^{6(100)} = {64}^{100}\)

By looking at the base numbers, we can tell which is the least and which is the greatest. The numbers from greatest to least is: \(3^{400} , 2^{600}, 25^{100} , 4^{200} , 2^{300}\)

- Daisy

Aug 25, 2018

#1
+3

Since there is no common base number, we will have to make a common exponent number. The GCF of all of these exponents is \(100\), so lets make all of the exponents \(100\). We have:

a) \({25}^{100}\)

b) \({2}^{3(100)} = {8}^{100}\)

c) \({3}^{4(100)} = {81}^{100}\)

d) \({4}^{2(100)} = {16}^{100}\)

e) \({2}^{6(100)} = {64}^{100}\)

By looking at the base numbers, we can tell which is the least and which is the greatest. The numbers from greatest to least is: \(3^{400} , 2^{600}, 25^{100} , 4^{200} , 2^{300}\)

- Daisy

dierdurst Aug 25, 2018